Subatomic Physics

504 Liquid Drop Model, Fermi Gas Model, Heavy Ions
The fact that only nuclides in a small band are stable is explained by another
term, the symmetry energy. The effect of the symmetry energy is best seen if the
mass excess ∆ is plotted against Z for all isobars characterized by a given value of
A. As an example, such a plot is shown in Fig. 16.2 for A = 127.
Figure 16.2: Mass excess ∆ as a function of
Z for A = 127.
Such a plot is analogous to a topographic
map, and Fig. 16.3 presents the contour
map of the binding energy in an N − Z
plane. Figure. 16.2 is the cross section
through the valley at the position indicated
in Fig. 16.3. The sides of the valley
are steep, and it is consequently difficult
experimentally to explore the valley to the
“top” because the nuclei are shortlived.
Some of these nuclei can be produced in
accelerators, separated and re-accelerated
in special facilities for short lived ions. (3)
The dashed countour lines in Fig. 16.3 indicate
the shorter lifetimes. The limits
of the region of stability are called “neutron
and proton drip lines”. Beyond these
the nuclei decay by the strong interactions
and the lifetimes are shorter than ∼ 10 −18
sec.
The figure appears like a cross section
through a deep valley; the isobar at the
bottom is the only stable one, and the
ones clinging to the steep sides tumble
down toward the bottom of the valley,
usually by emission of electrons or
positrons. The isobars with A = 127 are
not an isolated case; the mass excesses for
all other isobars also are shaped like cross
sections through a valley. Figure 5.20 can
therefore be brought into a more informative
form by adding a third dimension to
the plot: the binding energy or the mass
excess.
Figure 16.3: Sketch of binding energy B plotted
in form of a contour map in an N − Z
plane. The energy valley appears clearly; it
forms a canyon in the N −Z plane. The numbers
on the contour lines give the total binding
energy in MeV.
3 W. Henning, Nucl. Phys. A746, 3c (2004); J.A. Nolen, Nucl. Phys. A746, 9c (2004).